2024/09/04 by Yuly Billig, Billig, Yuly, Emile Bouaziz +1 · 1 citation
Mathematics · #17B10 (Secondary) #17B66 (Primary) 14F10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2409.02677
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study sheaves of modules for the Lie algebra of vector fields with the action of the algebra of functions, compatible via the Leibniz rule. A crucial role in this theory is played by the virtual jets of vector fields - jets that evaluate to a zero vector field under the anchor map. Virtual jets of vector fields form a vector bundle L+ whose fiber is Lie algebra \widehatL+ of vanishing at zero derivations of power series. We show that a sheaf of AV-modules is characterized by two ingredients - it is a module for L+ and an L+-charged D-module. For each rational finite-dimensional representation of \widehatL+, we construct a bundle of jet AV-modules. We also show that Rudakov modules may be realized as tensor products of jet modules with a D-module of delta functions.